All children who build sandcastles on the beach know that in addition to sand you also need to add a little water to prevent the structure from collapsing. But why is this? In an article which appeared today in Scientific ...

Real-time data that will be used in everything from weather forecasts to disaster response is now being beamed down to Earth from a cone-shaped appendage aboard the nation's newest Earth-observing satellite.

(Phys.org) -- In Isaac Newton's Principia Mathematica published in 1687, the man many consider the most brilliant mathematician of all time used a mathematical formula to describe the path taken by an object when it is thrown ...

(Phys.org) -- The vascular system of a leaf provides its structure and delivers its nutrients. When you light up that vascular structure with some fluorescent dye and view it using time-lapse photography, details begin to ...

Carmakers and airplane manufacturers are very particular when it comes to the weight of their models: the lighter they are, the less fuel they consume - and the less carbon dioxide they blow into the air. If a car loses 100 ...

Formula

In mathematics, a formula (plural: formulae or formulas) is an entity constructed using the symbols and formation rules of a given logical language.

In science, a formula is a concise way of expressing information symbolically (as in a mathematical or chemical formula), or a general relationship between quantities. Colloquial use of the term in mathematics often refers to a similar construct.

Such formulae are the key to solving an equation with variables. For example, determining the volume of a sphere requires a significant amount of integral calculus; but, having done this once, mathematicians can produce a formula to describe the volume in terms of some other parameter (the radius for example). This particular formula is:

Having obtained this result, and knowing the radius of the sphere in question, we can quickly and easily determine its volume. Note that the quantities V, the volume, and r the radius are expressed as single letters. This convention, while less important in a relatively simple formula, means that mathematicians can more quickly manipulate larger and more complex formulae.

Expressions are distinct from formulae in that they cannot contain an equals sign; whereas formulae are comparable to sentences, expressions are more like phrases.

In a general context, formulae are applied to provide a mathematical solution for real world problems. Some may be general: F = ma, which is one expression of Newton's second law, is applicable to a wide range of physical situations. Other formulae may be specially created to solve a particular problem; for example, using the equation of a sine curve to model the movement of the tides in a bay. In all cases however, formulae form the basis for all calculations.